However, to produce the negative gradient needed for calculations the inverse of temperature must be used instead of the temperature, this is shown below.
However, this does not provide the activation energy or the Arrhenius Constant of the reaction.
To determine the frequency factor (Arrhenius Constant) and the activation energy of the reaction the following equation must be used.
Where k= 1/time, A = the frequency factor, Ea= the activation energy, R = 8.314J K-1 and T = the temperature in Kelvin. However, not all the variables are known, therefore a graph of ln (k) on 1/T must be plotted. This equation is derived from the above equation and is shown below.
The y intercept on this graph will provide and the gradient of the graph will provide. The Graph of ln (k) over 1/T is shown below.
The equation for the graph above is in the form of y=mx + c. Where m is the gradient and c is the y intercept. Therefore, m = - (Ea/R) = -4421 and c = ln (A) = 8.37.
Activation Energy:
-4421 = - (Ea/R) where R = 8.314
- 4421 × 8.314 = -Ea
∴ Ea = 36760 J
= 36.76 KJ mol-1
Conclusion and Evaluation:
The activation energy calculated was 36.76 KJ mol-1. However, the theoretical activation energy for this reaction is defined as 52 KJ mol-1. This shows that there were problems with the experiment. Although the reaction rate discovered from the experiment differs from the theoretical reaction rate the reaction rate found from the experiment supports the experiment. This is because when the variables are plot into the equation the answer supports the data recorded. This is shown below.
Ea = 36760 J
R = 8.314 J
T = 300K
1/T = 0.0033
Ln (A) = 8.37
These values were taken from graphs and data tables shown above.
∴Ln (k) = 8.37 – (36760/8.314) × 0.0033
= -6.22
The value for ln(k) determined from recordings is -6.3.This shows that the equation answer differs by 0.1 units or 0.02%. This indicates that the experiment was accurate with minimal errors. However errors that did arise from the procedure of the experiment include an error in the recording of time due to human error. Additionally the recordings for each temperature were not repeated. This leads to inaccurate readings as the experiment may have outliers. Furthermore, repetitions of the experiment did not take place. This greatly reduces the accuracy of the experiment because it does not allow for the reduction of random errors. Furthermore, human error could have greatly affected this experiment due to the uncertainty of when the cross fully disappears. The errors caused by this error would be too random to correctly predict, therefore, it was not factored into any equations, tables or graphs. This could explain the variance of the found activation energy against the theoretically accepted activation energy.
To reduce these errors the method needs to be adjusted. Firstly, the same person needs to be used when recording the time. This makes the reaction time error of the reading of the time constant, as the same person with the same reaction time is used throughout the experiment. Additionally, more repeats of the experiment need to be made. This reduces the effect of an outlier as the readings are all averaged. The aim was successfully achieved because the relationship between temperature and reaction rate was successfully investigated. The relationship is shown through all the graphs and tables shown above. The first graph shows that there is an exponential relationship between the rate of reaction and the temperature. This means that as temperature increases the rate of reaction increases by a factor of approximately 2. It also shows that the reaction is second order. The second graph provides the negative gradient needed for the calculations and the third graph gives the data to find the activation energy. The R2 value showed on the third graph shows how accurate the line of best fit. An R2 value of 1 shows that the line of best fit perfectly matches the data points. Therefore, an R2 value of 0.9629 shows that the data points were accurate.
Bibliography:
Dr Terry Badran, Personal Communication
- Make sure uncertainties are correct
- Record raw temperature data in Celsius
- Indentify claims
- Significant figures in table and graphs
- Graphs only areas where data points are – don’t need to extend to y axis
- Equations in graphs
- Put errors and improvement s in table
- Always include repetition of trials in errors
- Use scientific notation for very large or very small numbers
